I can definitely build this system for you. I have already built several autodialer systems like this, with and without text-to-speech systems. All I will need is an example of the data from your patient scheduling system.
I will guide you on the selection of a VOIP provider (if needed), installation of the Linux base, install Asterisk, and then install the autodialer system.
I can also guide you on which text-to-speech system to use based on budget and quality.
I have been developing with and for Asterisk systems for 10+ years now and have extensive experience in many programming languages.
Feel free to contact me with any questions.